It was found that in addition to the removal of the floating matter, other processes also must be performed with the separator. It is e.g. sometimes necessary to completely empty the separator housing following the discharge of the sinking matter, and to clean it, if needed, in order to remove residues that could cause an anaerobic reaction of the separated matter. It can also be useful to discharge the separator content at least partially after the floating matter has been removed, in order to enable a control of the raking mechanisms that are possibly present in the separator for thickening the framed floating matter. A partial emptying is also useful if the aqueous phase is drained after the discharge of the floating matter, and if the sinking matter is removed only after this.